Problem: Which of the following numbers is a factor of 138? ${2,8,9,10,13}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $138$ by each of our answer choices. $138 \div 2 = 69$ $138 \div 8 = 17\text{ R }2$ $138 \div 9 = 15\text{ R }3$ $138 \div 10 = 13\text{ R }8$ $138 \div 13 = 10\text{ R }8$ The only answer choice that divides into $138$ with no remainder is $2$ $ 69$ $2$ $138$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $2$ are contained within the prime factors of $138$ $138 = 2\times3\times23 2 = 2$ Therefore the only factor of $138$ out of our choices is $2$. We can say that $138$ is divisible by $2$.